Waving a copy of the request before the UN General Assembly to huge applause, Abbas said he had submitted an "application for the admission of Palestine on the basis of the June 4, 1967 borders" with Jerusalem as its capital.
He also called for Secretary General Ban Ki-moon "to expedite transmittal of our request to the Security Council and I call upon the distinguished members of the Security Council to vote in favor of our full membership."
The Palestinian UN ambition was unlikely to materialize as the United States has vowed to veto the bid at the UN Security Council, where the move requires the backing of nine of the 15 council members.
But the Lebanese ambassador to the United Nations, Nawaf Salam, said that the Security Council would meet Monday afternoon to discuss the request.
In his speech, Abbas stressed he wished to resume direct peace talks with Israel despite the UN request which deeply angered Israel.
"Here I declare that the Palestine Liberation Organization is ready to return immediately to the negotiating table on the basis of the adopted terms of reference... and a complete cessation of settlement activities," Abbas told the UN General Assembly.
But he maintained previous peace talks were "smashed against the rocks of the positions of the Israeli government, which quickly dashed the hopes raised by the launch of negotiations last September."
Israeli Prime Minister Benjamin Netanyahu and Foreign Minister Avigdor Lieberman, both present in the UN headquarters at the time, shunned Abbas's speech after a spokesman for the premier said he regretted the Palestinian statehood move.
The Palestinian leader nevertheless sought to reassure the Israelis: "Our efforts are not aimed at isolating Israel or delegitimizing it; rather we want to gain legitimacy for the cause of the people of Palestine."
He branded the Jewish settlement activity in the occupied West Bank as "the primary cause for the failure of the peace process."
"This policy will destroy the chances of achieving a two-state solution upon which there is an international consensus," Abbas told the UN General Assembly after submitting a request for Palestinian as a UN member state.
"This settlement policy threatens to also undermine the structure of the Palestinian National Authority and even end its existence," he said.
"We only aim to delegitimize the settlement activities, the occupation and apartheid and the logic of ruthless force, and we believe that all the countries of the world stand with us in this regard," Abbas said in the historic speech.
Abbas won huge applause and a standing ovation Friday from some of the assembly as he entered the hall shortly after asking the UN to admit the state of Palestine.
There was also applause when he paid tribute to the late Palestinian leader Yasser Arafat, during his speech to the annual assembly meeting.
Speaking shortly after Abbas, Netanyahu also said he was extending a hand of peace but accused the Palestinians of refusing to resume talks, whose latest round broke down in September 2010.
And in the hours that followed the two leaders' addresses the international Quartet for Middle East peace -- the United States, the European Union, Russia and the United Nations -- said they wanted Israelis and Palestinians to resume peace talks within a month in a bid to reach a peace agreement by the end of 2012.
Copyright AFP (Agence France-Presse), 2011